Question

How is the graph of log (x – 5) translated from the graph of log x?

Answer 1

is shifted a units right from f(x)=log(x)

Answer 2

Answer:

The graph of y=logx shifts 5 units right to get the graph of y=log(x – 5).

Step-by-step explanation:

The parent log function is

$y=\log x$

The translation of the function is defined as

$y=\log (x+a)+b$                .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The given function is

$y=\log (x-5)$               .... (2)

From (1) and (2), we get

$a=-5,b=0$

Since a=-5<0, therefore the graph of y=logx shifts 5 units right to get the graph of y=log(x – 5).